Whereas a considerable body of works exists on the physics of melt extraction from the hot mantle at mid-oceanic ridges, melt migration through the colder continental lithosphere is less well understood. As 500 million people live in the vicinity of active volcanoes and the most dangerous volcanoes are located on continental lithosphere, it however remains an important topic for the Earth Sciences.
High precision U-Pb dating of batholiths seems to suggest that many of them are formed by an amalgamation of smaller melt pulses. Since those pulses presumably rose at approximately the same location of the lithosphere, it is likely that this changed (and likely weakened) the mechanical state of the lithosphere with time.
Here, I will discuss thermo-mechanical models of melt propagation through the cold mantle lithosphere to address the consequences of this mechanical weakening on melt transport. In addition, I will discuss (simple) models of granitic melt intrusion within the continental crust in which diking is incorporated in a parameterized manner and in which melt is emplaced in many pulses. The results of these models suggests that that both pulses and localized mechanical weakening is of key importance for magma transport. They also show that in other to understand magmatic transport systems, it is insufficient to only focus on the batholiths itself or on the batholith-volcano connection. Instead, magmatic systems are lithospheric-scale systems, and should be modelled as such.
In this respect, many unresolved questions remain and I will discuss some of those.

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